The asterisk inside the example block isn't escaped properly, and
appears as a header, leaving `#+begin_example` and `#+end_example` to
appear as regular text. It occurs in at least both the HTML and LaTeX
output. Here is a minimal example to reproduce the problem:

    * first section

    #+begin_example
    * I am not supposed to be a section
    #+end_example

    * second section

    #+begin_example
    Hello, world!
    #+end_example

This is using `emacs -Q`, so I've left off the current state
section. This also happens with Org commit
3c4cb7b296c78aafb0d6302a4075f1f1fa1c7e1c (`org-collect-keywords` was
causing me issues, so I'm not at HEAD).

Emacs  : GNU Emacs 27.0.91 (build 1, x86_64-pc-linux-gnu, GTK+ Version
3.24.20, cairo version 1.17.3)
 of 2020-05-17
Package: Org mode version 9.3 (release_9.3 @
/usr/share/emacs/27.0.91/lisp/org/)